Du Toit and Burdick [1]}, Park et al. [2]} approximate the integral in (REF ) as \(Vp(\textbf {x}_k,\textbf {s})\) , where \(V\)  is the 2D footprint (area) occupied by the robot. For this approximation, in [1]} it is assumed that the robot radius \(\varepsilon \)  is negligible and a point obstacle is considered for this derivation.
